Nonstationary Precipitation

Frequency Estimates for Texas

JAMES DOSS-GOLLIN

Rice Civil & Environmental Engineering

Yuchen Lu (Rice)

Benjamin Seiyon Lee (GMU)

John Nielsen-Gammon (TAMU)

Rewati Niraula (TWDB)

@AGU 2023, NH14B-07

for better or for worse,

IDF CURVES UNDERPIN RISK ASSESSMENT

James Doss-Gollin

Bates et al. (2021) fig. 8

Mark Wolfe/FEMA News

EXISTING GUIDANCE LEAVES GAPS

THE CLIMATE IS CHANGING BUT SAMPLING VARIABILITY IMPEDES TREND ESTIMATION

Fagnant et al. (2020): Rolling window estimates of the 100 year return level. Each line shows a different gauge from the same \(5^\circ \times 3^\circ\) region.

EARTH SYSTEM MODELS:

Better sample weather given climate

Physical constraints improve extrapolation

Limitations (drizzle bias, dynamics, etc.) motivate bias correction

still need a statistical model!

(EVEN WITH SOPHISTICATED TOOLS)

do we capture extremes and their trends?

Yuhao Liu, Guha Balakrishnan, Ashok Veeraraghavan, & James Doss-Gollin (in prep.): computer vision-based downscaling. (T) low-resolution input, (M) high-resolution model output, and (B) ground truth for 8 time steps.

NONSTATIONARY MODELS

NEED MORE PARAMETERS

Stationary: \(y(\mathbf{s}, t) \sim \text{GEV} \left( \mu(\mathbf{s}), \sigma(\mathbf{s}), \xi(\mathbf{s}) \right)\)

Nonstationary: \(y(\mathbf{s}, t) \sim \text{GEV} \left( \mu(\mathbf{s}, t), \sigma(\mathbf{s}, t), \xi(\mathbf{s}, t) \right)\)

Process-informed models condition parameters on climate indices \(\mathbf{x}(t)\): \[ \theta(\mathbf{s}, t) = \alpha + \underbrace{\sum_{j=1}^J \beta_j(\mathbf{s}) x_j(t)}_\text{additional parameters} \]

NONSTATIONARY MODELS

INCREASE ESTIMATION UNCERTAINTY

More parameters, same data more uncertainty (Serinaldi & Kilsby, 2015)

SPATIALLY VARYING COVARIATES

We model statistical parameters as latent spatial fields in a hierarchical Bayesian framework, leading to improved estimates.

Histogram showing the quantile of each observed annual maximum given the posterior predictive distribution for that location and year. For a perfect model, this will be uniformly distributed. Preliminary results.

HAZARD HAS ALREADY INCREASED

Change in 100 year return level in 2022 minus 1980 for (L) 1- and (R) 24-hour precipitation. Preliminary results.

HAZARD WILL FURTHER INCREASE

Posterior expected 100 year rainfall as a function of time. Preliminary results.

CONCLUSIONS

Can’t do statistical analysis without stats

Nonstationarity should be the default assumption

Need better stats (e.g., spatially varying covariates!) to fit nonstationary models

Sampling variability is immortal

For more, see Yuchen Lu’s poster H21T-1602 on Tuesday morning

References

Bates, P. D., Quinn, N., Sampson, C., Smith, A., Wing, O., Sosa, J., et al. (2021). Combined modeling of US fluvial, pluvial, and coastal flood hazard under current and future climates. Water Resources Research, 57(2), e2020WR028673. https://doi.org/10.1029/2020WR028673
Fagnant, C., Gori, A., Sebastian, A., Bedient, P. B., & Ensor, K. B. (2020). Characterizing spatiotemporal trends in extreme precipitation in Southeast Texas. Natural Hazards, 104(2), 1597–1621. https://doi.org/10.1007/s11069-020-04235-x
Serinaldi, F., & Kilsby, C. G. (2015). Stationarity is undead: Uncertainty dominates the distribution of extremes. Advances in Water Resources, 77, 17–36. https://doi.org/10.1016/j.advwatres.2014.12.013

@jdossgollin